First, I will first remove
the common factor of 3, taking the leading negative sign with it:

–6x^{2} + 15x + 36 = –3(2x^{2}
– 5x – 12)

Then I'll factor the remaining quadratic: 2x^{2}
– 5x – 12 = (x – 4)(2x + 3):

When I write down my
answer, I need to remember to include the –3 factor:

–6x^{2} +
15x + 36 = –3(x – 4)(2x
+ 3).

A disguised version of this
factoring-out-the-negative case is when they give you a backwards quadratic
where the squared term is subtracted. For example, if they give you something
like 6 + 5x + x^{2}, you would just reverse the quadratic
to put it back in the "normal" order, and then factor: 6 + 5x
+ x^{2} = x^{2} + 5x + 6 = (x + 2)(x
+ 3). You can do this because order doesn't matter in addition. In subtraction,
however, order does matter, and you need to be careful with signs.